We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Toward this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.
Bibliographical noteFunding Information:
Acknowledgments Yongjiang Guo is supported by the NSFC grants 10901023 and 11101050. Erjen Lefeber is supported by NWO-VIDI grant 639.072.072. The bulk of the work of Yoni Nazarathy on this paper was while he was affiliated with EURANDOM/Eindhoven University of Technology and partly supported by the same grant. Gideon Weiss is supported by Israel Science Foundation Grants 454/05 and 711/09.
- Control policies
- Fluid models
- Infinite virtual queues
- Lyapunov functions
- Multi-class queueing networks
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics